Problems after a leak

Hi there,

Sorry if this is the wrong sub-section, I'm new - it didn't seem to have a great fit anywhere really.

So my problem lies in an eyesore left by a leaky sky light. As the pictures show, even though the skylight has been fixed and we have a new roof (therefore no more leaking), the damage has been done. I'm unsure as to how to go about fixing it. Should I scrape off the paint that is falling and replaster and repaint? How about the ceiling?